Joint detection and estimation refers to deciding between two or more hypotheses and, depending on the test outcome, simultaneously estimating the unknown parameters of the underlying distribution. This problem is investigated in a sequential framework under mild assumptions on the underlying random process. We formulate an unconstrained sequential decision problem, whose cost function is the weighted sum of the expected run-length and the detection/estimation errors. Then, a strong connection between the derivatives of the cost function with respect to the weights, which can be interpreted as Lagrange multipliers, and the detection/estimation errors of the underlying scheme is shown. This property is used to characterize the solution of a closely related sequential decision problem, whose objective function is the expected run-length under constraints on the average detection/estimation errors. We show that the solution of the constrained problem coincides with the solution of the unconstrained problem with suitably chosen weights. These weights are characterized as the solution of a linear program, which can be solved using efficient off-the-shelf solvers. The theoretical results are illustrated with two example problems, for which optimal sequential schemes are designed numerically and whose performance is validated via Monte Carlo simulations.2. The hypothesis H i , i = 0, 1, as well as the random parameter Θ i do not change during the observation period of X N .3. A sufficient static t n (x n ) in a state space (E t , E t ) exists such thatThe sufficient statistic has a transition kernel of the formand some initial statistic t 0 .4. The two hypotheses are separable, i.e.,5. The second order moment of the random parameter Θ exists and is finite, i.e., E[Θ 2 ] <∞ .Note that this implies, that the conditional second order moment E[Θ 2 | A] exist and is finite for all events A with non-zero probability.

No abstract

<div>In contrast to iodine(I)-based halogen bond donors, </div><div>iodine(III)-derived ones have only been used as Lewis acidic organocatalysts in a handful of examples, and in all cases they acted in a monodentate fashion. Herein, we report the first application of a bidentate bis(iodolium) salt as organocatalyst in a Michael and a nitro-Michael addition reaction as well as in a Diels-Alder reaction that had not been activated by noncovalent organocatalysts before. In all cases, the performance of this bidentate XB donor distinctly </div><div>surpassed the one of arguably the currently strongest iodine(I)-based organocatalyst. Bidentate coordination to the substrate was corroborated by a structural analysis and by DFT calculations of the transition states. Overall, the catalytic activity of the bis(iodolium) system approaches that of strong Lewis acids like BF3.</div>

No abstract